Properties

Label 27.3.f
Level 27
Weight 3
Character orbit f
Rep. character \(\chi_{27}(2,\cdot)\)
Character field \(\Q(\zeta_{18})\)
Dimension 30
Newforms 1
Sturm bound 9
Trace bound 0

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Defining parameters

Level: \( N \) = \( 27 = 3^{3} \)
Weight: \( k \) = \( 3 \)
Character orbit: \([\chi]\) = 27.f (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 27 \)
Character field: \(\Q(\zeta_{18})\)
Newforms: \( 1 \)
Sturm bound: \(9\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(27, [\chi])\).

Total New Old
Modular forms 42 42 0
Cusp forms 30 30 0
Eisenstein series 12 12 0

Trace form

\(30q \) \(\mathstrut -\mathstrut 6q^{2} \) \(\mathstrut -\mathstrut 6q^{3} \) \(\mathstrut -\mathstrut 6q^{4} \) \(\mathstrut -\mathstrut 15q^{5} \) \(\mathstrut -\mathstrut 18q^{6} \) \(\mathstrut -\mathstrut 6q^{7} \) \(\mathstrut -\mathstrut 9q^{8} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(30q \) \(\mathstrut -\mathstrut 6q^{2} \) \(\mathstrut -\mathstrut 6q^{3} \) \(\mathstrut -\mathstrut 6q^{4} \) \(\mathstrut -\mathstrut 15q^{5} \) \(\mathstrut -\mathstrut 18q^{6} \) \(\mathstrut -\mathstrut 6q^{7} \) \(\mathstrut -\mathstrut 9q^{8} \) \(\mathstrut -\mathstrut 3q^{10} \) \(\mathstrut -\mathstrut 6q^{11} \) \(\mathstrut -\mathstrut 15q^{12} \) \(\mathstrut -\mathstrut 6q^{13} \) \(\mathstrut -\mathstrut 15q^{14} \) \(\mathstrut -\mathstrut 9q^{15} \) \(\mathstrut -\mathstrut 18q^{16} \) \(\mathstrut -\mathstrut 9q^{17} \) \(\mathstrut +\mathstrut 63q^{18} \) \(\mathstrut -\mathstrut 3q^{19} \) \(\mathstrut +\mathstrut 213q^{20} \) \(\mathstrut +\mathstrut 132q^{21} \) \(\mathstrut -\mathstrut 42q^{22} \) \(\mathstrut +\mathstrut 120q^{23} \) \(\mathstrut +\mathstrut 144q^{24} \) \(\mathstrut -\mathstrut 15q^{25} \) \(\mathstrut -\mathstrut 90q^{27} \) \(\mathstrut -\mathstrut 12q^{28} \) \(\mathstrut -\mathstrut 168q^{29} \) \(\mathstrut -\mathstrut 243q^{30} \) \(\mathstrut +\mathstrut 39q^{31} \) \(\mathstrut -\mathstrut 360q^{32} \) \(\mathstrut -\mathstrut 207q^{33} \) \(\mathstrut +\mathstrut 54q^{34} \) \(\mathstrut -\mathstrut 252q^{35} \) \(\mathstrut -\mathstrut 360q^{36} \) \(\mathstrut -\mathstrut 3q^{37} \) \(\mathstrut -\mathstrut 84q^{38} \) \(\mathstrut +\mathstrut 15q^{39} \) \(\mathstrut -\mathstrut 33q^{40} \) \(\mathstrut +\mathstrut 228q^{41} \) \(\mathstrut +\mathstrut 486q^{42} \) \(\mathstrut -\mathstrut 96q^{43} \) \(\mathstrut +\mathstrut 639q^{44} \) \(\mathstrut +\mathstrut 477q^{45} \) \(\mathstrut -\mathstrut 3q^{46} \) \(\mathstrut +\mathstrut 399q^{47} \) \(\mathstrut +\mathstrut 453q^{48} \) \(\mathstrut -\mathstrut 78q^{49} \) \(\mathstrut +\mathstrut 303q^{50} \) \(\mathstrut +\mathstrut 36q^{51} \) \(\mathstrut -\mathstrut 9q^{52} \) \(\mathstrut -\mathstrut 54q^{54} \) \(\mathstrut -\mathstrut 12q^{55} \) \(\mathstrut -\mathstrut 393q^{56} \) \(\mathstrut -\mathstrut 192q^{57} \) \(\mathstrut +\mathstrut 129q^{58} \) \(\mathstrut -\mathstrut 474q^{59} \) \(\mathstrut -\mathstrut 846q^{60} \) \(\mathstrut +\mathstrut 138q^{61} \) \(\mathstrut -\mathstrut 900q^{62} \) \(\mathstrut -\mathstrut 585q^{63} \) \(\mathstrut -\mathstrut 51q^{64} \) \(\mathstrut -\mathstrut 411q^{65} \) \(\mathstrut -\mathstrut 423q^{66} \) \(\mathstrut +\mathstrut 354q^{67} \) \(\mathstrut +\mathstrut 99q^{68} \) \(\mathstrut +\mathstrut 99q^{69} \) \(\mathstrut +\mathstrut 489q^{70} \) \(\mathstrut +\mathstrut 315q^{71} \) \(\mathstrut +\mathstrut 720q^{72} \) \(\mathstrut -\mathstrut 66q^{73} \) \(\mathstrut +\mathstrut 321q^{74} \) \(\mathstrut +\mathstrut 255q^{75} \) \(\mathstrut +\mathstrut 258q^{76} \) \(\mathstrut +\mathstrut 201q^{77} \) \(\mathstrut +\mathstrut 180q^{78} \) \(\mathstrut +\mathstrut 30q^{79} \) \(\mathstrut +\mathstrut 36q^{81} \) \(\mathstrut -\mathstrut 12q^{82} \) \(\mathstrut -\mathstrut 33q^{83} \) \(\mathstrut -\mathstrut 588q^{84} \) \(\mathstrut -\mathstrut 261q^{85} \) \(\mathstrut -\mathstrut 258q^{86} \) \(\mathstrut -\mathstrut 279q^{87} \) \(\mathstrut -\mathstrut 642q^{88} \) \(\mathstrut +\mathstrut 72q^{89} \) \(\mathstrut +\mathstrut 288q^{90} \) \(\mathstrut +\mathstrut 96q^{91} \) \(\mathstrut -\mathstrut 3q^{92} \) \(\mathstrut +\mathstrut 591q^{93} \) \(\mathstrut -\mathstrut 861q^{94} \) \(\mathstrut +\mathstrut 681q^{95} \) \(\mathstrut +\mathstrut 270q^{96} \) \(\mathstrut -\mathstrut 582q^{97} \) \(\mathstrut +\mathstrut 882q^{98} \) \(\mathstrut +\mathstrut 513q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(27, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
27.3.f.a \(30\) \(0.736\) None \(-6\) \(-6\) \(-15\) \(-6\)